A Test for detecting Structural Breakdowns in Markets using Eigenvalue Decompositions

Abstract

Correlations among stock returns during volatile markets differ substantially compared to those from quieter markets. During times of financial crisis, it has been observed that traditional dependency in global markets breaks down. However, such an upheaval in dependency structure happens over a span of several months, with the breakdown coinciding with a major bankruptcy or sovereign default. Even though risk managers generally agree that identifying these periods of breakdown is important, there are few statistical methods to test for significant breakdowns. The purpose of this paper is to propose a simple test to detect such structural changes in global markets. This test relies on the assumption that asset price follows a Geometric Brownian Motion. We test for a breakdown in correlation structure using eigenvalue decomposition. We derive the asymptotic distribution under the null hypothesis and apply the test to stock returns. We compute the power of our test and compare it with the power of other known tests. Our test is able to accurately identify the times of structural breakdown in real-world stock returns. Overall we argue, despite the parsimony and simplicity in the assumption of Geometric Brownian Motion, our test can perform well to identify the breakdown in dependency of global markets.